They can. Marriage and birth certificates establish the relationships that TD status depends on, so names, dates and spellings need to match the principal's records. TD may be available to a spouse and unmarried children under twenty-one, with steps that vary by nationality.
Match the family record to the principal's file
Preserve accents, surname changes and the names actually recorded on each document. Explain a genuine discrepancy with supporting records instead of altering it in translation. Agree consistent terminology with each translator; one translator is not a legal requirement.
TD permits study but does not authorize employment. Ask about a proposed remote activity or unpaid placement specifically rather than assuming it falls outside work restrictions. Work through the family records in the same order every time: the document that establishes the relationship, the document that establishes each person's identity, then anything explaining a difference between them.
A civil-status certificate issued years after the event is ordinary and is not itself a discrepancy. Where a surname was recorded differently at marriage, the act recording that change is what settles it, so obtain that document rather than annotating a translation. Ask in plain terms what each dependent intends to do before the file is assembled, because the answer decides which questions have to be researched instead of assumed.